That said, none of the other games released could be considered "spin-offs", since they all tell an integral part of a larger over-arching story. It's like trying to say anything that isn't Avengers-branded is an MCU spin-off.

The main 3 games tell the story of the main character Sora in his battle against the main villain. The side stories are well integrated into the main story, but they are still side stories. Even the article I cited used Kingdom Hearts as an example of a series with tons of spin-offs.

And no, your MCU example doesn't work. MCU is a universe. If Avengers were the main series, then yes, the Iron man movies, Captain America movies, etc would all be spinoffs of Avengers. They all take place within the MCU. If you don't consider Avengers the main series, but just a series that takes place within the MCU, then all the series are just IPs with stories that interrelate. Harry Potter would be another interesting example here. The first 8 movies were a standalone series, and then the "Fantastic Beasts" series was made, which is a spinoff to the first series, even though it contains story details related to events in the first series.

What I don't get is why everyone is so damn upset by this. Who cares how the games are classified? That doesn't decrease their legitimacy, or their fun.

The three numbered titles tell the perspective of Sora in a much larger plot that, especially in KH3, requires the context of the non-numbered titles.

Those "side stories" aren't side stories. They're integral, especially to KH3. There are literal hours of that game that makes zero sense without playing the non-numbered titles.

There's literally not a single part of the MCU analogy that doesn't work. They're different sections of the same story in the same universe about different characters that all coalesce into a single story about the same overarching plot. Outside of the non-canon Verizon game I mentioned, the only title that even comes close to qualifying as a "spin off" is Union X, but the events of KH3 have shown more now than ever that Union X is setting the series up for the next arc.

Because when people think about spin-offs, they think about junk like Raving Rabids, Fable II Pub Games, and Shadow the Hedgehog.